Can I wrap a video as material on a blender object?
In Cycles, in your Material Image Texture Node, make sure you enter the Number of Frames and the Start Frame of the video you want Blender to extract.  Movie should be selected automatically.  Check the Cyclic and Auto Refresh  checkboxes (Note: You must be in Rendered Mode to see the frame advance with Cycles.).

Auto Refresh:  Automatically refresh images on frame changes.
Cyclic: Start over and repeats after the last frame to create a continuous loop.



In BI, it's the same process but it's under Textures (the gif above was rendered using Blender Render). Note: Texture and Material Mode seem to work fine with frame advance in BI as well as Rendered: